In
mathematics,
binomial coefficients are a family of positive
integers that occur as
coefficients in the
binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by
n and
k is usually written
. It is the
coefficient of the
x k term in the
polynomial expansion of the
binomial power (1 +
x)
n. Under suitable circumstances the value of the coefficient is given by the expression . Arranging binomial coefficients into rows for successive values of
n, and in which
k ranges from 0 to
n, gives a triangular array called
Pascal's triangle.